The origin of degeneracies and crossings in the 1d Hubbard model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyse in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter-independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter-independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wavefunctions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter-independent symmetry.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

An extended Cahn-Hilliard model for interfaces with cubic anisotropy

For studying systems with a cubic anisotropy in interfacial energy sigma, we extend the Cahn-Hilliard model by including in it a fourth-rank term, namely, gamma (ijlm) [partial derivative (2) c/(partial derivativex(i) partial derivativex(j))] [partial derivative (2) c/(partial derivativex(l) partial derivativex(m))]. This term leads to an additional linear term in the evolution equation for the composition parameter field. It also leads to an orientation-dependent effective fourth-rank coefficient gamma ([hkl]) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative gamma ([hkl]) is to increase both sigma and interfacial width w, each of which, upon suitable scaling, is related to gamma ([hkl]) through a universal scaling function. In this model, sigma is a differentiable function of interface orientation (n) over cap, and does not exhibit cusps; therefore, the equilibrium particle shapes (Wulff shapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners become rounded, and their shapes tend towards the Wulff shape with increasing particle size.

Nonlinear Finite-Element Modeling of Batter Piles under Lateral Load

In this paper, a finite-element model is developed in which the nonlinear soil behavior is represented by a hyperbolic relation for static load condition and modified hyperbolic relation, which includes both degradation and gap for a cyclic load condition. Although batter piles are subjected to lateral load, the soil resistance is also governed by axial load, which is incorporated by considering the P-Δ moment and geometric stiffness matrix. By adopting the developed numerical model, static and cyclic load analyses are performed adopting an incremental-iterative procedure where the pile is idealized as beam elements and the soil as elastoplastic spring elements. The proposed numerical model is validated with published laboratory and field pile test results under both static and cyclic load conditions. This paper highlights the importance of the degradation factor and its influence on the soil resistance-displacement (p-y) curve, number of cycles of loading, and cyclic load response.

A new beam finite element for the analysis of functionally graded materials

A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the first-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing differential equations is used to construct interpolating polynomials for the element formulation. Consequently, the stiffness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine different stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral difference of functionally graded material beam with pure metal or pure ceramic beams. (C) 2003 Elsevier Science Ltd. All rights reserved.

A note on surface water waves for finite depth in the presence of an ice-cover

A class of I boundary value problems involving propagation of two-dimensional surface water waves, associated with water of uniform finite depth, against a plane vertical wave maker is investigated under the assumption that the surface is covered by a thin sheet of ice. It is assumed that the ice-cover behaves like a thin isotropic elastic plate. Then the problems under consideration lead to those of solving the two-dimensional Laplace equation in a semi-infinite strip, under Neumann boundary conditions on the vertical boundary as well as on one of the horizontal boundaries, representing the bottom of the fluid region, and a condition involving upto fifth order derivatives of the unknown function on the top horizontal ice-covered boundary, along with the two appropriate edge-conditions, at the ice-covered corner, ensuring the uniqueness of the solutions. The mixed boundary value problems are solved completely, by exploiting the regularity property of the Fourier cosine transform.

Finite element simulation of BAW propagation in inhomogeneous plate due to piezoelectric actuation

A set of finite elements (FEs) is formulated to analyze wave propagation through inhomogeneous material when subjected to mechanical, thermal loading or piezo-electric actuation. Elastic, thermal and electrical properties of the materials axe allowed to vary in length and thickness direction. The elements can act both as sensors and actuators. These elements are used to model wave propagation in functionally graded materials (FGM) and the effect of inhomogeneity in the wave is demonstrated. Further, a surface acoustic wave (SAW) device is modeled and wave propagation due to piezo-electric actuation from interdigital transducers (IDTs) is studied.

Study of the CP property of the Higgs boson at a photon collider using gamma gamma -> t(t)over-bar -> lX

We study the possible effects of CP violation in the Higgs sector on t (t) over bar production at a gammagamma collider. These studies are performed in a model-independent way in terms of six form factors {R(S-gamma), J(S-gamma), R(P-gamma), J(P-gamma), S-t, P-t} which parametrize the CP mixing in the Higgs sector, and a strategy for their determination is developed. We observe that the angular distribution of the decay lepton from t/(t) over bar produced in this process is independent of any CP violation in the tbW vertex and hence best suited for studying CP mixing in the Higgs sector. Analytical expressions are obtained for the angular distribution of leptons in the c.m. frame of the two colliding photons for a general polarization state of the incoming photons. We construct combined asymmetries in the initial state lepton (photon) polarization and the final state lepton charge. They involve CP even (x's) and odd (y's) combinations of the mixing parameters. We study limits up to which the values of x and y, with only two of them allowed to vary at a time, can be probed by measurements of these asymmetries, using circularly polarized photons. We use the numerical values of the asymmetries predicted by various models to discriminate among them. We show that this method can be sensitive to the loop-induced CP violation in the Higgs sector in the minimal supersymmetric standard model.

A Coalition game model for spectrum pooling in wireless data access networks

We consider a setting in which several operators offer downlink wireless data access services in a certain geographical region. Each operator deploys several base stations or access points, and registers some subscribers. In such a situation, if operators pool their infrastructure, and permit the possibility of subscribers being served by any of the cooperating operators, then there can be overall better user satisfaction, and increased operator revenue. We use coalitional game theory to investigate such resource pooling and cooperation between operators.We use utility functions to model user satisfaction, and show that the resulting coalitional game has the property that if all operators cooperate (i.e., form a grand coalition) then there is an operating point that maximizes the sum utility over the operators while providing the operators revenues such that no subset of operators has an incentive to break away from the coalition. We investigate whether such operating points can result in utility unfairness between users of the various operators. We also study other revenue sharing concepts, namely, the nucleolus and the Shapely value. Such investigations throw light on criteria for operators to accept or reject subscribers, based on the service level agreements proposed by them. We also investigate the situation in which only certain subsets of operators may be willing to cooperate.

Swam Intelligent Based Inverse Model for Laboratory Double Reservoir Diffusion Experiments

Theoretical approaches are of fundamental importance to predict the potential impact of waste disposal facilities on ground water contamination. Appropriate design parameters are, in general, estimated by fitting the theoretical models to a field monitoring or laboratory experimental data. Double-reservoir diffusion (Transient Through-Diffusion) experiments are generally conducted in the laboratory to estimate the mass transport parameters of the proposed barrier material. These design parameters are estimated by manual parameter adjusting techniques (also called eye-fitting) like Pollute. In this work an automated inverse model is developed to estimate the mass transport parameters from transient through-diffusion experimental data. The proposed inverse model uses particle swarm optimization (PSO) algorithm which is based on the social behaviour of animals for finding their food sources. Finite difference numerical solution of the transient through-diffusion mathematical model is integrated with the PSO algorithm to solve the inverse problem of parameter estimation.The working principle of the new solver is demonstrated by estimating mass transport parameters from the published transient through-diffusion experimental data. The estimated values are compared with the values obtained by existing procedure. The present technique is robust and efficient. The mass transport parameters are obtained with a very good precision in less time

Modified lattice model for mode-I fracture analysis of notched plain concrete beam using probabilistic approach

A modified lattice model using finite element method has been developed to study the mode-I fracture analysis of heterogeneous materials like concrete. In this model, the truss members always join at points where aggregates are located which are modeled as plane stress triangular elements. The truss members are given the properties of cement mortar matrix randomly, so as to represent the randomness of strength in concrete. It is widely accepted that the fracture of concrete structures should not be based on strength criterion alone, but should be coupled with energy criterion. Here, by incorporating the strain softening through a parameter ‘α’, the energy concept is introduced. The softening branch of load-displacement curves was successfully obtained. From the sensitivity study, it was observed that the maximum load of a beam is most sensitive to the tensile strength of mortar. It is seen that by varying the values of properties of mortar according to a normal random distribution, better results can be obtained for load-displacement diagram.

Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

Groundwater Management in India:Physical, Institutional and Policy Alternatives

Groundwater constitutes a vital natural resource for sustaining India’s agricultural economy and meeting the country’s social, ecological and environmental goals. It is a unique resource, widely available, providing security against droughts and yet it is closely linked to surface-water resources and the hydrological cycle. Its availability depends on geo-hydrological conditions and characteristics of aquifers, from deep to alluvium, sediment crystalline rocks to basalt formations; and agro-climate from humid to subhumid and semi-arid to arid. Its reliable supply, uniform quality and temperature, relative turbidity, pollution-safe, minimal evaporation losses, and low cost of development are attributes making groundwater more attractive compared to other resources. It plays a key role in the provision of safe drinking water to rural populations. For example, already almost 80% of domestic water use in rural areas in India is groundwater-supplied, and much of it is being supplied to farms, villages and small towns. Inadequate control of the use of groundwater, indiscriminate application of agrochemicals and unrestrained pollution of the rural environment by other human activities make groundwater usage unsustainable, necessitating proper management in the face of the twin demand for water of good quality for domestic supply and adequate supply for irrigation, ensuring equity, efficiency and sustainability of the resource. Groundwater irrigation has overtaken surface irrigation in the early 1980s, supported by well energization. It is estimated that there are about 24 million energised wells and tube wells now and it is driven by demand rather than availability, evident through the greater occurrence of wells in districts with high population densities. Apart from aquifer characteristics, land fragmentation and landholding size are the factors that decide the density of wells. The ‘rise and fall’ of local economies dependent on groundwater can be summarized as: the green revolution of 1980s, groundwaterbased agrarian boom, early symptoms of groundwater overdraft, and decline of the groundwater socio-ecology. The social characteristics and policy interventions typical of each stage provide a fascinating insight into the human-resource dynamics. This book is a compilation of nine research papers discussing various aspects of groundwater management. It attempts to integrate knowledge about the physical system, the socio-economic system, the institutional set-up and the policy environment to come out with a more realistic analysis of the situation with regard to the nature, characteristics and intensity of resource use, the size of the economy the use generates, and the negative socioeconomic consequences. Complex variables addressed in this regard focusing on northern Gujarat are the stock of groundwater available in the region, its hydrodynamics, its net outflows against inflows, the economics of its intensive use (particularly irrigation in semi-arid and arid regions), its criticality in the regional hydroecological regime, ethical aspects and social aspects of its use. The first chapter by Dinesh Kumar and Singh, dwells on complex groundwater socio-ecology of India, while emphasizing the need for policy measures to address indiscriminate over-exploitation of dwindling resources. The chapter also explores the nature of groundwater economy and the role of electricity prices on it. The next chapter on groundwater issue in north Gujarat provides a description of groundwater resource characteristics followed by a detailed analysis of the groundwater depletion and quality deterioration problems in the region and their undesirable consequences on the economy, ecosystem health and the society. Considering water-buyers and wellowning farmers individually, a methodology for economic valuation of groundwater in regions where its primary usage is in agriculture, and as assessment of the groundwater economy based on case studies from north Gujarat is presented in the fourth chapter. The next chapter focuses on the extent of dependency of milk production on groundwater, which includes the water embedded in green and dry fodder and animal feed. The study made a realistic estimate of irrigation water productivity in terms of the physics and economics of milk production. The sixth chapter analyses the extent of reduction in water usage, increase in yield and overall increase in physical productivity of alfalfa with the use of the drip irrigation system. The chapter also provides a detailed synthesis of the costs and benefits associated with the use of drip irrigation systems. A linear programmingbased optimization model with the objective to minimize groundwater use taking into account the interaction between two distinct components – farming and dairying under the constraints of food security and income stability for different scenarios, including shift in cropping pattern, introduction of water-efficient crops, water- saving technologies in addition to the ‘business as usual’ scenario is presented in the seventh chapter. The results show that sustaining dairy production in the region with reduced groundwater draft requires crop shifts and adoption of water-saving technologies. The eighth chapter provides evidences to prove that the presence of adequate economic incentive would encourage farmers to adopt water-saving irrigation devices, based on the findings of market research with reference to the level of awareness among farmers of technologies and the factors that decide the adoption of water-saving technologies. However, now the marginal cost of using electricity for agricultural pumping is almost zero. The economic incentives are strong and visible only when the farmers are either water-buyers or have to manage irrigation with limited water from tube-well partnerships. The ninth chapter explores the socio-economic viability of increasing the power tariff and inducing groundwater rationing as a tool for managing energy and groundwater demand, considering the current estimate of the country’s annual economic loss of Rs 320 billion towards electricity subsidy in the farm sector. The tenth chapter suggests private tradable property rights and development of water markets as the institutional tool for achieving equity, efficiency and sustainability of groundwater use. It identifies the externalities for local groundwater management and emphasizes the need for managing groundwater by local user groups, supported by a thorough analysis of groundwater socio-ecology in India. An institutional framework for managing the resource based on participatory approach that is capable of internalizing the externalities, comprising implementation of institutional and technical alternatives for resource management is also presented. Major findings of the analyses and key arguments in each chapter are summarized in the concluding chapter. Case studies of the social and economic benefits of groundwater use, where that use could be described as unsustainable, are interesting. The benefits of groundwater use are outlined and described with examples of social and economic impacts of groundwater and the negative aspects of groundwater development with the compilation of environmental problems based on up-to-date research results. This publication with a well-edited compilation of case studies is informative and constitutes a useful publication for students and professionals.

Three-Dimensional Site Characterization Model Using Artificial Neural Networks

This research is designed to develop a new technique for site characterization in a three-dimensional domain. Site characterization is a fundamental task in geotechnical engineering practice, as well as a very challenging process, with the ultimate goal of estimating soil properties based on limited tests at any half-space subsurface point in a site.In this research, the sandy site at the Texas A&M University's National Geotechnical Experimentation Site is selected as an example to develop the new technique for site characterization, which is based on Artificial Neural Networks (ANN) technology. In this study, a sequential approach is used to demonstrate the applicability of ANN to site characterization. To verify its robustness, the proposed new technique is compared with other commonly used approaches for site characterization. In addition, an artificial site is created, wherein soil property values at any half-space point are assumed, and thus the predicted values can compare directly with their corresponding actual values, as a means of validation. Since the three-dimensional model has the capability of estimating the soil property at any location in a site, it could have many potential applications, especially in such case, wherein the soil properties within a zone are of interest rather than at a single point. Examples of soil properties of zonal interest include soil type classification and liquefaction potential evaluation. In this regard, the present study also addresses this type of applications based on a site located in Taiwan, which experienced liquefaction during the 1999 Chi-Chi, Taiwan, Earthquake.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.